J. N. Reddy

Bio: J. N. Reddy is an academic researcher from Texas A&M University. The author has contributed to research in topics: Finite element method & Plate theory. The author has an hindex of 106, co-authored 926 publications receiving 66940 citations. Previous affiliations of J. N. Reddy include Instituto Superior Técnico & National University of Singapore.

Optimal design of laminated piezocomposite energy harvesting devices considering stress constraints

Abstract: Summary Energy harvesting devices are smart structures capable of converting the mechanical energy (generally, in the form of vibrations) that would be wasted otherwise in the environment into usable electrical energy. Laminated piezoelectric plate and shell structures have been largely used in the design of these devices because of their large generation areas. The design of energy harvesting devices is complex, and they can be efficiently designed by using topology optimization methods (TOM). In this work, the design of laminated piezocomposite energy harvesting devices has been studied using TOM. The energy harvesting performance is improved by maximizing the effective electric power generated by the piezoelectric material, measured at a coupled electric resistor, when subjected to a harmonic excitation. However, harmonic vibrations generate mechanical stress distribution that, depending on the frequency and the amplitude of vibration, may lead to piezoceramic failure. This study advocates using a global stress constraint, which accounts for different failure criteria for different types of materials (isotropic, piezoelectric, and orthotropic). Thus, the electric power is maximized by optimally distributing piezoelectric material, by choosing its polarization sign, and by properly choosing the fiber angles of composite materials to satisfy the global stress constraint. In the TOM formulation, the Piezoelectric Material with Penalization and Polarization material model is applied to distribute piezoelectric material and to choose its polarization sign, and the Discrete Material Optimization method is applied to optimize the composite fiber orientation. The finite element method is adopted to model the structure with a piezoelectric multilayered shell element. Numerical examples are presented to illustrate the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.

Nonlocal continuum crystal plasticity with internal residual stresses

Abstract: We derive a three-dimensional constitutive theory accounting for length-scale dependent internal residual stresses in crystalline materials that develop due to a non-homogeneous spatial distribution of the excess dislocation (edge and screw) density. The second-order internal stress tensor is derived using the Beltrami stress function tensor φ that is related to the Nye dislocation density tensor. The formulation is derived explicitly in a three-dimensional continuum setting for elastically isotropic materials. The internal stresses appear as additional resolved shear stresses in the crystallographic visco-plastic constitutive law for individual slip systems. Using this formulation, we investigate two boundary value problems involving single crystals under symmetric double slip. In the first problem, the response of a geometrically imperfect specimen subjected to monotonic and cyclic loading is investigated. The internal stresses affect the overall strengthening and hardening under monotonic loading, which is mediated by the severity of initial imperfections. Such imperfections are common in miniaturized specimens in the form of tapered surfaces, fillets, fabrication induced damage, etc., which may produce strong gradients in an otherwise nominally homogeneous loading condition. Under cyclic loading the asymmetry in the tensile and compressive strengths due to this internal stress is also strongly influenced by the degree of imperfection. In the second example, we consider simple shear of a single crystalline lamella from a layered specimen. The lamella exhibits strengthening with decreasing thickness and increasing lattice incompatibility with shearing direction. However, as the thickness to internal length-scale ratio becomes small the strengthening saturates due to the saturation of the internal stress. Finally, we present the extension of this approach for crystalline materials exhibiting elastic anisotropy, which essentially depends on the appropriate Green function within φ.

Ordered rate constitutive theories in Lagrangian description for thermoviscoelastic solids without memory

Abstract: This paper presents ordered rate constitutive theories in Lagrangian description for compressible as well as incompressible homogeneous, isotropic thermoviscoelastic solid matter with memory in which the material derivative of order m of the deviatoric stress tensor and heat vector are functions of temperature, temperature gradient, time derivatives of the conjugate strain tensor up to any desired order n, and the material derivatives of up to order m−1 of the stress tensor. The thermoviscoelastic solids described by these theories are called ordered thermoviscoelastic solids with memory due to the fact that the constitutive theories are dependent on orders m and n of the material derivatives of the conjugate stress and strain tensors. The highest orders of the material derivative of the conjugate stress and strain tensors define the order of the thermoviscoelastic solid. The constitutive theories derived here show that the material for which these theories are applicable have fading memory. As is well known, the second law of thermodynamics must form the basis for deriving constitutive theories for all deforming matter (to ensure thermodynamic equilibrium during evolution), since the other conservation and balance laws are independent of the constitution of the matter. The entropy inequality expressed in terms of Helmholtz free energy density \({\Phi}\) does not provide a mechanism to derive a constitutive theory for the stress tensor when its argument tensors are stress and strain rates in addition to others. With the decomposition of the stress tensor into equilibrium and deviatoric stress tensors, the constitutive theory for the equilibrium stress tensor is deterministic from the entropy inequality. However, for the deviatoric stress tensor, the entropy inequality requires a set of inequalities to be satisfied but does not provide a mechanism for deriving a constitutive theory. In the present work, we utilize the theory of generators and invariants to derive rate constitutive theories for thermoviscoelastic solids with memory. This is based on axioms and principles of continuum mechanics. However, we keep in mind that these constitutive theories must satisfy the inequalities resulting from the second law of thermodynamics. The constitutive theories for heat vector q are derived: (i) strictly using conditions resulting from the entropy inequality; (ii) using the theory of generators and invariants with admissible argument tensors that are consistent with the stress tensor as well as the theories in which simplifying assumptions are employed which yield much simplified theories. It is shown that the rate theories presented here describe thermoviscoelastic solids with memory. Mechanisms of dissipation and memory are demonstrated and discussed, and the derivation of memory modulus is presented. It is shown that simplified forms of the general theories presented here result in constitutive models that may resemble currently used constitutive models but are not the same. The work presented here is not to be viewed as extension of the current constitutive models; rather, it is a general framework for rate constitutive theories for thermoviscoelastic solids with memory based on the physics and derivations that are consistent within the framework of continuum mechanics and thermodynamics. The purpose of the simplified theories presented in the paper is to illustrate possible simplest theories within the consistent framework presented here.

Influence of the homogenization scheme on the bending response of functionally graded plates

Abstract: Functionally graded materials (FGM) are an advanced class of engineering composites constituting of two or more distinct phase materials described by continuous and smooth varying composition of material properties in the required direction. In this work, the effect of the material homogenization scheme on the flexural response of a thin to moderately thick FGM plate is studied. The plate is subjected to different loading and boundary conditions. The formulation is developed based on the first-order shear deformation theory. The mechanical properties are assumed to vary continuously through the thickness of the plate and obey a power-law distribution of the volume fraction of the constituents. The variation of volume fraction through the thickness is computed using two different homogenization techniques, namely rule of mixtures and Mori–Tanaka scheme. Comparative studies have been carried out to demonstrate the efficiency of the present formulation. The results obtained from the two techniques have been compared with the analytical solutions available in the literature. In addition to the above a parametric study bringing out the effect of boundary conditions, loads, and power-law index has also been presented.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Robot dynamics and control

Abstract: From the Publisher: This self-contained introduction to practical robot kinematics and dynamics includes a comprehensive treatment of robot control. Provides background material on terminology and linear transformations, followed by coverage of kinematics and inverse kinematics, dynamics, manipulator control, robust control, force control, use of feedback in nonlinear systems, and adaptive control. Each topic is supported by examples of specific applications. Derivations and proofs are included in many cases. Includes many worked examples, examples illustrating all aspects of the theory, and problems.

A Simple Higher-Order Theory for Laminated Composite Plates

Abstract: A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.